EASY
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In a non-uniform circular motion of a body, its radial acceleration remains constant in magnitude but the magnitude of tangential acceleration changes with time.

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Important Questions on Motion in a Plane

EASY

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of m s-2) is of the order of :

HARD
A particle is moving in a circular path of radius a under the action of an attractive potential U=-k2r2. Its total energy is:
EASY
A particle is performing uniform circular motion along the circumference of a circle of diameter 50 cm with frequency 2 Hz. The acceleration of the particle in m s-2 is:
MEDIUM
A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes 14th of the original in time t and n revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are (Angular retardation is uniform)
EASY
The quantity that remains constant in uniform circular motion is :
MEDIUM

A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0 . The mass is attached to a string which passes through a smooth hole in plane as shown.

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The tension in the string is increased gradually and finally m moves in a circle of radius R02. The final value of the kinetic energy is:

HARD
A uniform rod of length l  is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from the axis, then which of the following graphs depicts it most closely?
MEDIUM
A uniform rod of mass 0.5 kg and length 0.5 m is suspended at its ends by means of two light inextensible strings so that the rod is horizontal. If one of the strings is cut, then the angular acceleration of the rod is (Acceleration due to gravity =10 m s-2)
MEDIUM
A mass attached to one end of a string crosses topmost point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( g= gravitational acceleration)
EASY
A car goes around uniform circular track of radius R at a uniform speed v once in every T seconds. The magnitude of the centripetal acceleration is ac. If the car now goes uniformly around a larger circular track of radius 2R and experiences a centripetal acceleration of magnitude 8ac. Then, its time period is
MEDIUM
One end of a straight uniform 1 m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30o from the horizontal (see figure). Its angular speed when it hits the table is given as n rad s-1 , where n is an integer. The value of n is ____________
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EASY
In Circular motion which one is correct
HARD
A particle moves such that its position vector rt=cosωt i^+sinωt j^, where ω is a constant and t is time. Then which of the following statements is true for the velocity vt and acceleration at of the particle:
EASY
A body moving along a circular path due to a centripetal force having constant magnitude is an example of motion with ___ .
MEDIUM
A uniform solid sphere of radius R and radius of gyration K about an axis passing through the centre of mass, is rolling without slipping. Then the fraction of total energy associated with its rotation will be
MEDIUM
A thin metallic disc is rotating with constant angular velocity about a vertical axis that is perpendicular to its plane and passes through its centre. The rotation causes the free electrons in the disc to redistribute. Assume that, there is no external electric or magnetic field. Then,
HARD

Two blocks of masses m and 2 m connected by a massless string move along concentric horizontal circles on a horizontal frictionless table with O as fixed point as shown in the figure. If T is the period of motion, the tension in the longer part of the string is (Neglect the dimensions of the blocks when compared with the lengths of the string).

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HARD
A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the nth power of R. If the period of rotation of the particle is T, then:
MEDIUM
A boy moving along a circular path of radius 10 m completes 3/4th of the circle in 10 sec. The magnitude of speed and velocity are
MEDIUM
Why is the motion of a body moving with a constant speed around a circular path said to be accelerated?